In an electron microscope, the object to be observed is illuminated by an electron beam. The radiation reflected by the object, or transmitted through the object, or secondary electrons emitted by the object, are focused to form a magnified picture of the object by means of electromagnetic lenses. The best achievable resolution (limiting resolution or information limit) of the object structure is physically limited by partial temporal (longitudinal) coherence of the electron beam and, in modern microscopes this is in the range of less than one angstrom. From (K. J. Hansen, L. Trepte, Der Einfluss von Strom-und Spannungsschwankungen, sowie der Energiebreite der Strahlelektronen auf Kontrastubertragung und Auflosung des Elektronenmikroskops [The influence of current and voltage fluctuations and the energy width of beam electrons on electron microscope contrast transmission and resolution], Optik 32, 519 (1971)) and (K. Ishizuka, Contrast transfer of crystal images in TEM, Ultramicroscopy 5, 55-65 (1980)) it is known that partial temporal coherence of the electron beam is substantially caused by the finite energy width of the beam electrons, temporal fluctuations in the accelerating voltage, and temporal fluctuations in the current in the electromagnetic lenses.
The limiting resolution is of fundamental importance for assessing the reliability of pictures taken with electron microscopes. The limiting resolution is defined by the defocus spread.
The defocus spread, and thus indirectly the limiting resolution, is traditionally determined based on diffractograms of thin amorphous objects, under central illumination of the object. A diffractogram is an optically or digitally produced Fourier transform of an electron-optical image. The intensity distribution of these diffractograms depends on the concrete effective cross-sections for the diffraction of electrons in the object, the object thickness, and the modulation transfer function of the detector used for imaging. Since these parameters are, in practice, largely unknown, the diffractograms cannot be quantitatively evaluated, which is disadvantageous.
The “Young's fringe” method for improving the visibility of imaging contrasts is known from (J. Frank, Nachweis von Objektbewegungen im lichtoptischen Diffraktogramm von elektronenmikroskopischen Aufnahmen [Detection of object movements in photo-optical diffractograms of electron microscope images], Optik 30, 171 (1969)). Here, two consecutively taken pictures of a thin amorphous object are superimposed with a slight displacement. The diffractogram of this superimposition shows a conspicuous line pattern. The spatial frequency at which this line pattern can no longer be differentiated from the noise defines the limiting resolution of the electron microscope. This is evaluated based on qualitative visibility criteria.
A disadvantage is that this method is dependent on a subjective assessment by the observer. In addition, the visibility of the line pattern depends on the amplification properties of the detector and also on whether the intensities in the diffractogram are shown on a linear or logarithmic scale. The limiting resolution determined with this method is therefore subject to very large errors that cannot be limited.
Furthermore, the traditional “Young's fringe method” has the disadvantage that it cannot be used to differentiate between linear and non-linear contrasts, and that non-linear contrast fractions under certain conditions can simulate a far better limiting resolution than is actually present. With the traditional Young's fringe method, significant systematic errors of up to 50% of the actual limiting resolution may occur, particularly at low accelerating voltages, due to the non-linear effect.